The conventional exercise machines are generally formed of two hand grips, which are fastened fixedly or pivotally with the machine body to facilitate the balancing of the body of an exerciser. Such a conventional hand grip structure as described above is defective in design in that it is ineffective in providing a user of the machine with a means to balance his or her body at such time when the user of the machine is in motion. In other words, the conventional hand grips are capable of acting to balance the body of the user of the machine at the time when the exerciser is in a stationary state. The case in point is the conventional leg exercising machine comprising two hand grips capable of moving along an oval track. The swinging motion of the hand grips cannot be properly coordinated with the adjustment in dynamic balance of the exerciser. In addition, the swinging range of the hand grips, the onset of the swinging motion of the hand grips, and the timing of the swinging motion of the hand grips cannot be properly modified.